Question

quadrilateral abcd is dilated by a scale factor centered at the origin to create quadrilateral abcd as shown on the coordinate plane. what is the scale factor of the dilation?

Explanation:

Step1: Select a point and its image

Let's take point C(0, 8) and its image C'(0, 4).

Step2: Calculate the scale - factor formula

The scale - factor \(k\) for a dilation centered at the origin is given by \(k=\frac{y_{image}}{y_{original}}\) (for points on the y - axis, similar for x - axis). Here, \(k = \frac{4}{8}\).

Step3: Simplify the ratio

\(k=\frac{4}{8}=\frac{1}{2}\).

Answer:

C. \(\frac{1}{2}\)